In the production of paper cups from segments of paper material, it is known to produce these cups from paper that is coated on one or both sides with polyethylene (PE). Such coated paper segments can be joined to each other by sealing, that is to say, by heating the plastic layer. A primer or an adhesion promoter is used at critical sites for increasing the sealability. Such a primer is a type of adhesive and substantially consists of a low-viscosity aqueous polymer solution. Such a primer is applied to the paper segment, for example, with the aid of felt saturated with the primer. The low viscosity of the primer causes the machine to be soiled relatively severely, and the felt used for applying the primer is also subjected to considerable wear and has consequently to be replaced at regular intervals. It is further known to pre-break paper segments, whether coated or uncoated, at a segment edge before they are wound up on a folding mandrel, in order to facilitate the winding process and particularly the production of an overlap on the breaking mandrel. Uncoated paper segments are coated with adhesive in the region of the overlap and then glued to form a sleeve.